secx - sinxtanx

Answer 1

1/cosx - sinx/cosx = (1-sinx)/cosx

I guess you could go further, recalling that sin and cos are complementary functions, and get

(1-sinx)/cosx
= (1-cos(90-x))/sin(90-x)
= tan((90-x)/2)
= tan(45 - x/2)

Answer 2

Oops -- my bad!

secx - sinx tanx
= 1/cosx - sin^2x/cosx
= (1-sin^2x)/cosx
= cos^2x/cosx
= cosx